Solve 1/x^-4*1/x^5

$$\frac{ 1 }{ { x }^{ -4 } } \times \frac{ 1 }{ { x }^{ 5 } }$$

Evaluate

$$\frac{1}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{1}{x^{-4}}\times \frac{1}{x^{5}}$$

To raise a power to another power, multiply the exponents.

$$x^{-4\left(-1\right)}x^{5\left(-1\right)}$$

Multiply -4 times -1.

$$x^{4}x^{5\left(-1\right)}$$

Multiply 5 times -1.

$$x^{4}x^{-5}$$

To multiply powers of the same base, add their exponents.

$$x^{4-5}$$

Add the exponents 4 and -5.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

Multiply \frac{1}{x^{-4}} times \frac{1}{x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{-4}x^{5}})$$

To multiply powers of the same base, add their exponents. Add -4 and 5 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{1}})$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})$$

The derivative of ax^{n} is nax^{n-1}.

$$-x^{-1-1}$$

Subtract 1 from -1.

$$-x^{-2}$$